Critical temperature of the superconducting transition in the generalized Hubbard model

Miguel Citeli de Freitas

Demetrio Vilardi, Pietro M. Bonetti, Walter Metzner

N. A. Kuleeva, É. Z. Kuchinskiǐ, Michael V. Sadovskii

We present a brief review of our studies of disorder influence upon Ginzburg-Landau expansion coefficients in Anderson-Hubbard model with attraction in the framework of the generalized DMFT + Σ approximation. A wide range of attractive potentials U is considered from weak coupling limit, where superconductivity is described by BCS model, to the limit of very strong coupling, where superconducting transition is related to the Bose-Einstein condensation of compact Cooper pairs, which are formed at temperatures significantly higher than the superconducting transition temperature, as well as the wide range of disorders from weak to strong, when the system is in the vicinity of Anderson transition. For the same range of parameters we study in detail the temperature behavior of orbital and paramagnetic upper critical field H c2 ( T ), which demonstrates the anomalies due both to the growth of attractive potential and to the effects of strong disordering.

Xin-Zhong Yan

A. N. Bogolyubov, А. В. Москаленко

É. Z. Kuchinskiǐ, N. A. Kuleeva, Michael V. Sadovskii

We study disorder effects upon the temperature behavior of the upper critical magnetic field in an attractive Hubbard model within the generalized DMFT+Σ approach. We consider the wide range of attraction potentials U —from the weak coupling limit, where superconductivity is described by BCS model, up to the strong coupling limit, where superconducting transition is related to Bose–Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures significantly higher than superconducting transition temperature, as well as the wide range of disorder—from weak to strong, when the system is in the vicinity of Anderson transition. The growth of coupling strength leads to the rapid growth of H c 2 ( T ), especially at low temperatures. In BEC limit and in the region of BCS–BEC crossover H c 2 ( T ), dependence becomes practically linear. Disordering also leads to the general growth of H c 2 ( T ). In BCS limit of weak coupling increasing disorder lead both to the growth of the slope of the upper critical field in the vicinity of the transition point and to the increase of H c 2 ( T ) in the low temperature region. In the limit of strong disorder in the vicinity of the Anderson transition localization corrections lead to the additional growth of H c 2 ( T ) at low temperatures, so that the H c 2 ( T ) dependence becomes concave. In BCS–BEC crossover region and in BEC limit disorder only slightly influences the slope of the upper critical field close to T c . However, in the low temperature region H c 2 ( T may significantly grow with disorder in the vicinity of the Anderson transition, where localization corrections notably increase H c 2 ( T = 0) also making H c 2 ( T ) dependence concave.